The Power of Words


[highly speculative, probably wrong, maybe patronizing, etc.]


Does it matter whether we describe kids as being “gifted” or as “ready for more”?

Is it just harmless to describe things as crazy, or lame?

Should we refrain from using terms like misconception, mistake, or error when describing a student’s thinking of mathematical work?

Here is a perspective — I don’t think it’s my own — from which the answers to these questions are, yes, it matters, no, it’s not harmless, and of course we should refrain from those terms.

The reason is not so much because of how those words will impact others. Because the words are routine and normal, they wouldn’t really draw attention from other people, unless those people have already been woken up to the true implications of those words. The language isn’t harmless, but it doesn’t necessarily harm anybody.

The first source of harm is what the words you choose do to you. The words you use are sort of like an infection, from this perspective. They dive deep into your psyche and start unconsciously impacting the way you see things. They form the seeds of unconscious bias, silently impacting the way you see the world. If you’re always talking about mistakes and errors that a kid makes, that’s going to shape the grooves of your mind, making it easier to fall into noticing the negatives. Ditto with ableist language. The Sapir-Whorf hypothesis is true, and serious.

The second source of harm is about what you’re not doing when you don’t guard your language, which is you don’t correct your biases. The point is that word choice is a discipline, a moral discipline. Focusing intently on the words you use is an active way of cultivating a thoughtful, less-biased personality.

How? Say that you’re looking at a piece of student work, and you’re trying to describe it. You see something that from a certain perspective is mathematically inaccurate. You reach for a word. You think, hmm, should I call this a ‘mistake’? And you have a moment where you reflect and say, hey, I should not focus on what this kid does not know, I should think about what they can do. Repeat that reflection on word choice a dozen times a day, hundreds of times a month. Reflecting on word choice can change a person.


Spring is here, and it’s math education conference week in the US. And, as usual, I’m feeling a contradictory slush of mixed feelings about sitting it out — relief that I don’t have to go and jealousy towards those who can.

Whether at conferences or following along at home, the main thing I feel is loneliness and alienation from the profession at large. This isn’t even necessarily a criticism of the math education profession. I just feel out of sync with things, that’s all. Things that lots and lots of other people find inspiring or useful, I just don’t find useful.

The flip side is true also, by the way. There are lots of things that I find meaningful and inspiring about teaching that generally don’t get much airtime in these conferences. Meaning, I’m not some sort of humorless scold, incapable of inspiration or fun. I guess there really isn’t any way to prove this and I am doth protesting too much but I think it’s true. Friends, family: a little support here??

I’m not exactly sure how to describe the things at conferences that feel orthogonal to the way I think. I think there are three big things that don’t fit with me naturally:

  1. expressing laws of teaching (e.g. do not teach by telling, ban worksheets and timed tests)
  2. inflating the stakes (e.g. mathematical violence)
  3. managing word choice (e.g. misconception, mistake)

Some time, over the next week, I’m going to see a slide from a conference presentation declaring “Let’s ban talk of misconceptions — it’s mathematical violence!” and I am going to be incredibly triggered and have to remind myself that I’m the one with the problem, not the speaker.


Are words powerful? Yes and no, I guess is what I’d say.

I had been ready to dismiss the Sapir-Whorf hypothesis (that language determines thought), but Douglas Hofstadter gives me pause:

I myself was once most disdainful of this hypothesis, but over time came to realize how deeply human thought — even my own! — is channeled by habit and thus, in the last accounting, by the repertoire of mental chunks (i.e., perceptual attractors) that are available to the thinker. I now think that it is high time for the Sapir-Whorf hypothesis to be reinstated, at least in its milder forms.

(To a lesser extent George Lakoff gives me pause.)

I remain skeptical that self-consciously changing the language someone else uses could impact their thinking. Like, suppose that you actually could actually ban or mandate language. (Not legally, but as a social matter we definitely can do this.) If you really think that language choice unconsciously impacts your own thinking or the thinking of others, then (modulo some unsavory side-effects) you should probably think that a ban or a mandate would reduce harmful biases. People will use better words, the words will have a better impact on their psyche, and as a result their biases will be improved.

But psychological biases are strong, and reinforced by the strong forces of society and culture. Can they really be reduced by the unconscious, subtle grooving of word choice? And without a reflective, conscious effort to change one’s habits? I remain skeptical.

But maybe word choice can improve oneself. If it does, I think it would be in the way I outlined above, as a reflective, moral practice that allows the speaker to frequently reflect on their thoughts and actions.

In other words, I can see how word choice can function as a moral practice that resembles a lot of the religious practices I uphold. Does eating matzah on Passover make you a better person? Of course not, but it could give you a chance to. And it also serves an important social function, centering a community around a shared practice.


When I was in high school, I remember there was a poster outside my classroom. It exhorted us to guard our tongues and refrain from lashon hara, evil speech, gossip, mean remarks, etc.

There were people I knew who were exceptionally cautious to follow these Jewish laws of speech. These laws were only articulated fairly recently in the Jewish legal game, in 1873, by Rabbi Israel Meir Kagan, but they were entirely widespread when I was in yeshiva. These friends of mine lived in a state of mild panic, in fear they would accidentally utter a bit of unnecessary gossip.

(Complicating things, Kagan also says that accidentally listening to forbidden speech is forbidden, so those who kept these laws carefully had to always be on guard against someone saying something that they shouldn’t hear. To be really safe, you really end up just having fewer conversations.)

There are all sorts of exceptions and guidelines for the rules, but what Kagan changed, for a sliver of the population, was the basic assumption: speech isn’t neutral, and what you express might be forbidden.

Even in high school, this didn’t fit with me. I mean, I certainly felt guilty about how I spoke. But I was a kid that liked to make people laugh. It’s my go-to social coping strategy, and has been for three decades or so. As a student, I tried very hard to stay away from meanness, but, well, let’s just say that Kagan didn’t have a chapter on jokes. The entire enterprise was perilously close to forbidden.

I do believe that I should try not to harm people with my words, and that’s as far as I go with Kagan. I’m not scrupulous about this, just as I’m not scrupulous with my language in general. I try to be scrupulous about other things, and I do think that they “matter” more for me.

But who am I to begrudge anyone their discipline, the thing that stops them in their tracks, helps them to think about themselves and their bad habits? Everyone needs a discipline, and guarding one’s language seems pretty good to me.